Write the Euler's equations for the rotational motion of a rigid body with one point fixed, under the action of torque N. Apply these equations to discuss the rotational motion of a symmetrical top in the absence of any force other than the reaction at the fixed point.
An observer S_1 sees two bodies A and B having equal rest mass approach each other with equal but opposite velocities 4c/5. To a second observe S_2, the body A is at rest. What us the velocity of the body B as seen by observe S_2? What are the kinetic energies of the body B in the frames of S_1 and S_2?
Write the Lagrange's equation for a system of particles which is acted upon by Conservative forces. What is a cyclic coordinate ? Show that the generalized momentum conjugate to a cyclic coordinate is conserved.
Explain Meissner effect and Josephson effect. Describe their applications in the field of superconductivity.
(i) Show that a negative logic OR gate is like a positive logic AND gate. (ii) Distinguish between Hadrons and Leptons.
What are the main applications of JFET? Discuss their advantages over bipolar transistors. Explain the working of n-channel JFET with the help of a schematic diagram.
Write down the characteristics of an ideal operational amplifier. Explain the term virtual ground. Draw a circuit diagram showing virtual ground in an operational amplifier.
(i) Discuss the variation of free carrier concentration with temperature for an intrinsic and extrinsic semiconductors. (ii) Explain the effect of negative and positive voltage feedback on an amplifier characteristics.
(i) What is the lowest non zero angular momentum for an elementary particle? Name at least three elementary particles having such an angular momentum. (ii) Write the spectral symbol of the term with S= 1/2, J = 5/2 and g = 6/7.
(i) Explain how neutrino was discovered from the [[UNCLEAR]]-decay of radioactive nuclei. (ii) Show that for a cubic lattice, the difference between the successive h, k, l planes is given by d_{h,k,l} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}
Explain shell model of the nucleus. Give evidence for nuclear shell structure. What are the limitations of the shell model?
(i) Explain why a neutral particle such as neutron possesses a finite value of magnetic moment, and how it is determined. (ii) Write down the electronic configuration of {}^7\text{Li}, \, {}^{13}\text{C} \quad \text{and} \quad {}^{25}\text{Mg} in the ground state of the nuclear shell model.
Which conservation laws are obeyed in nuclear reactions? Explain the significance of Q value of a nuclear reaction.
Distinguish between particle and antiparticle. How antiparticles were discovered?
Mention the conservation laws for strong, electromagnetic, and weak interactions.
(i) Treating CH molecule as an united atom, derive its resultant molecular electronic states. (ii) Calculate the moment of inertia of HCl molecule from the expression u_{\text{HCl}} = 20.68 (J+1), where J = 0, 1, 2, \dots
(i) A sample is irradiated by a 5000 Å\ radiation to give a Raman line at 5050.5 Å. Calculate the Raman frequency. (ii) Explain, both red and violet degraded bands have been observed in electronic band systems, but rotation-vibration spectra show bands degraded to red only.
Write the electronic configuration of mercury (Z = 80). Obtain the spectral term for the normal and the first excited configuration of the atom.
Derive an expression for the spin-orbit interaction energy in one electron system. Calculate the energy separation between the levels {}^2P_{1/2} and {}^2P_{3/2}.
Explain the nature, origin and significance of 21 cm hydrogen line.
